A single failure time distribution (FTD) may not be a good model for describing the system characteristics in case failures patterns are subjected to many causes. And, this suggests strongly that the population is not homogeneous but rather is made up of several subpopulations mixed in unknown proportions. Since, instantaneous/ immediate failures are a natural occurrence and such failures usually discard the assumption of a unimodel distribution and hence the usual method of modeling and inference procedures may not be accurate in practice such failures are called inliers. The inconsistency of such life data is modeled using a non-standard mixture of distributions by considering the FTD as Lindley distribution. Further, likelihood estimation of the unknown parameters of model along with Uniformly Minimum Variance Unbiased Estimator (UMVUE) for various parametric functions, wherever possible is done. Various estimators and characteristics are studied with the support of numerical examples.